N-CN. Complex Numbers
- No tasks yet illustrate this standard.
N-CN.A. Perform arithmetic operations with complex numbers.
N-CN.A.1. Know there is a complex number $i$ such that $i^2 = -1$, and every complex number has the form $a + bi$ with $a$ and $b$ real.
N-CN.A.2. Use the relation $i^2 = -1$ and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
N-CN.A.3. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
- No tasks yet illustrate this standard.
N-CN.B. Represent complex numbers and their operations on the complex plane.
N-CN.B.4. Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
N-CN.B.5. Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, $(-1 + \sqrt{3} i)^3 = 8$ because $(-1 + \sqrt3 i)$ has modulus $2$ and argument $120^\circ$.
N-CN.B.6. Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
- No tasks yet illustrate this standard.